arXiv subjects

Tor G. J. Myklebust

Publications and source records attributed to Tor G. J. Myklebust.

3 recordsLinked to original sources

arXiv2015

Quantum Walks on Generalized Quadrangles

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of $S^+(U^3)$, a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We probabilistically compute the spectrum of the line intersection graphs of two non-isomorphic generalized quadrangles of order $(5^2,5)$ under this matrix and thus provide strongly regular counter-examples to the conjecture.

math.CO↗

arXiv2015

Computing accurate Horner form approximations to special functions in finite precision arithmetic

In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such implementations. This heuristic takes a certain restricted specification of program structure and the desired error properties as input and takes explicit account of roundoff error during evaluation.

math.NA↗

arXiv2015

Solving maximum cut problems by simulated annealing

This paper gives a straightforward implementation of simulated annealing for solving maximum cut problems and compares its performance to that of some existing heuristic solvers. The formulation used is classical, dating to a 1989 paper of Johnson, Aragon, McGeoch, and Schevon. This implementation uses no structure peculiar to the maximum cut problem, but its low per-iteration cost allows it to find better solutions than were previously known for 40 of the 89 standard maximum cut instances tested within a few minutes of computation.

math.OC↗